# Constant of a series from Integration

• Apr 25th 2011, 11:35 PM
xEnOn
Constant of a series from Integration
When integrating a series, the constant from the integration is evaluated as part of the summation or is it as a constant "outside" of the whole summation?

Say I have http://quicklatex.com/cache3/ql_3fff...260c3ea_l3.png

Then is the result equals to this: http://quicklatex.com/cache3/ql_124f...583f875_l3.png ?

Or is the result equals to this: http://quicklatex.com/cache3/ql_7b7e...e90c54a_l3.png ?

Thanks!
• Apr 25th 2011, 11:38 PM
alexmahone
Either way is correct.

The C in your second equation equals the sum of C's in your first equation.
• Apr 25th 2011, 11:46 PM
xEnOn
But how would it be the same?

In the first one, if say after some working, I found out that C=5. Then there is a summation of 5 for infinity times(which results in infinity) and then plus the summation of Xn.
But in the second one, if C=5, it would just be the summation of Xn and then plus 5, wouldn't it?
• Apr 26th 2011, 12:16 AM
alexmahone
Quote:

Originally Posted by xEnOn
But how would it be the same?

In the first one, if say after some working, I found out that C=5. Then there is a summation of 5 for infinity times(which results in infinity) and then plus the summation of Xn.
But in the second one, if C=5, it would just be the summation of Xn and then plus 5, wouldn't it?

The C's in your first equation probably form a convergent sequence, whose sum is the C in your second equation.
• Apr 26th 2011, 12:50 AM
Prove It
The sum of constants is still a constant...